Lecture 3b— Introduction to semiconductors

ECE 4833 - Dr. Alan DoolittleGeorgia Tech
Lecture 3
Introduction to Semiconductors and Energy Bandgaps

Solar Cells
Why do the electrons flow when light is present but not flow when light is not present?
Answer, Energy Bandgap (very important concept).

For metals, the electrons can jump from the valence orbits (outermost core energy levels of the atom) to any position within the crystal (free to move throughout the crystal) with no extra energy needed to be suppliedFor insulators, it is VERY DIFFICULT for the electrons to jump from the valence orbits and requires a huge amount of energy to free the electron from the atomic core.For semiconductors, the electrons can jump from the valence orbits but does require a small amount of energy to free the electron from the atomic core.
Classifications of Electronic Materials

Semiconductor materials are a sub-class of materials distinguished by the existence of a range of disallowed energies between the energies of the valence electrons (outermost core electrons) and the energies of electrons free to move throughout the material.The energy difference (energy gap or bandgap) between the states in which the electron is bound to the atom and when it is free to conduct throughout the crystal is related to the bonding strength of the material, its density, the degree of ionicity of the bond, and the chemistry related to the valence of bonding.High bond strength materials (diamond, SiC, AlN, GaN etc...) tend to have large energy bandgaps.Lower bond strength materials (Si, Ge, etc...) tend to have smaller energy bandgaps.

More formally, the energy gap is derived from the Pauli exclusion principle, where no two electrons occupying the same space, can have the same energy. Thus, as atoms are brought closer towards one another and begin to bond together, their energy levels must split into bands of discrete levels so closely spaced in energy, they can be considered a continuum of allowed energy. Strongly bonded materials tend to have small interatomic distances between atoms. Thus, the strongly bonded materials can have larger energy bandgaps than do weakly bonded materials.

Material Classifications based on Bonding MethodBonds can be classified as metallic, Ionic, Covalent, and van der Waals.

Consider the case of the group 4 elements, all** covalently bonded
Element Atomic Radius/Lattice Constant Bandgap(How closely spaced are the atoms?)
C 0.91/3.56 Angstroms 5.47 eV
Si 1.46/5.43 Angstroms 1.12 eV
Ge 1.52/5.65 Angstroms 0.66 eV
-Sn 1.72/6.49 Angstroms ~0.08 eV*
Pb 1.81/** Angstroms Metal
*Only has a measurable bandgap near 0K
**Different bonding/Crystal Structure due to unfilled higher orbital states

Classifications of Electronic MaterialsTypes of Semiconductors:Elemental: Silicon or Germanium (Si or Ge)Compound: Gallium Arsenide (GaAs), Indium Phosphide (InP), Silicon Carbide (SiC), CdS and many others
Note that the sum of the valence adds to 8, a complete outer shell. I.E. 4+4, 3+5, 2+6, etc...

Compound Semiconductors: Offer high performance (optical characteristics, higher frequency, higher power) than elemental semiconductors and greater device design flexibility due to mixing of materials.
Binary: GaAs, SiC, etc...
Ternary: AlxGa1-xAs, InxGa1-xN where 0

Material Classifications based on Crystal Structure
Amorphous MaterialsNo discernible long range atomic order (no detectable crystal structure). Examples are silicon
dioxide (SiO2), amorphous-Si, silicon nitride (Si3N4), and others. Though usually thought of as less perfect than crystalline materials, this class of materials is extremely useful.Polycrystalline Materials
Material consisting of several domains of crystalline material. Each domain can be oriented differently than other domains. However, within a single domain, the material is crystalline. The size of the domains may range from cubic nanometers to several cubic centimeters. Many semiconductors are polycrystalline as are most metals.
Crystalline MaterialsCrystalline materials are characterized by an atomic symmetry that repeats spatially. The shape of
the unit cell depends on the bonding of the material. The most common unit cell structures are diamond, zincblende (a derivative of the diamond structure), hexagonal, and rock salt (simple cubic).
Increasing structural quality and increasing efficiency (performance)

Chemical Bonding Determines the
Bandgap

Comparison of the Hydrogen Atom and Silicon Atom
Hydrogen
Silicon
...3,2,1,arg2/2/tan,
6.13)4(2 220
4
nandechelectronqhtconsplanksmasselectronmwhere
neV
nqmEnergy
o
oelectronHydrogen
n=1: Complete Shell2 s electrons
n=2: Complete Shell2 2s electrons6 2p electrons
n=3:2 3s electronsOnly 2 of 6 3p electrons
4 empty states
4 Valence Shell Electrons

Pauli Exclusion Principle
Only 2 electrons, of spin+/-1/2, can occupy the same energy state at the same point in space.

Banding of Discrete states and the Simplified Model
T=0K
EC or conduction band
EV or valence band
Band Gap where no states
exist

4 electrons available for sharing (covalent bonding) in outer shell of atoms

Ec
Ev
No Holes valence band means no hole conduction is possible
No electrons in conduction band means no electron conduction
is possible
Band Occupation at Low Temperature (0 Kelvin)
For (Ethermal=kT)=0

+
Ec
Ev
Electron free to move in conduction band
Hole free to move in valence band
Band Occupation at Higher Temperature (T>0 Kelvin)
For (Ethermal=kT)>0

+
For (Ethermal=kT)>0
Carrier Movement Under Bias
Direction of Current Flow
Ec
Ev
Hole movement in valence band

+
Ec
Ev
For (Ethermal=kT)>0

+
Ec
Ev
For (Ethermal=kT)>0 QuickTime Movie

Ec
Ev
The valance band may have ~4e22 cm-3 valence electrons participating in the bonding processes holding the crystal together.
The valance band might only have ~1e6 to 1e19 cm-3 holes in the valence band (missing valence electrons). Thus, it is easier to account for the influence of the holes by counting the holes directly as apposed to counting very small changes in the valence electron concentrations.
Example: If there are 1e 22 cm-3 atoms in a crystal with each atom having 4 valence electrons. What is the difference in valence electron concentration for 1e12 holes verses 1e13 cm-3 holes?
Answer: 4 x 1e22 cm-3 -1e12 cm-3 = 3.9999999999e22cm-3 verses
4 x 1e22 cm-3 -1e13 cm-3 = 3.999999999e22cm-3
For accounting reasons keeping track of holes is easier!
Clarification of confusing issues:Holes and Electrons

Clarification of confusing issues:Holes and ElectronsTerminology
Electrons: Sometimes referred to as conduction electrons: The electrons in the conduction band that are free to move throughout the crystal.
Holes: Missing electrons normally found in the valence band (or empty states in the valence band that would normally be filled).
If we talk about empty states in the conduction band, we DO NOT call them holes! This would be confusing. The conduction band h

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